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Description
Modeling Anomalous Diffusion: From Statistics to MathematicsThis book focuses on modeling the anomalous diffusion phenomena, being ubiquitous in the natural world. Both the microscopic models (stochastic processes) and macroscopic models (partial differential equations) have been built up. The relationships between the two kinds of models are clarified, and based on these models, some statistical observables are analyzed. From statistics to mathematics, the built models show their power with their associated
This book focuses on modeling the anomalous diffusion phenomena, being ubiquitous in the natural world. Both the microscopic models (stochastic processes) and macroscopic models (partial differential equations) have been built up. The relationships between the two kinds of models are clarified, and based on these models, some statistical observables are analyzed. From statistics to mathematics, the built models show their power with their associated applications.
This book is important for students to develop basic skills to be able to succeed in their future research. In addition to introducing the related models or methods, it also provides the corresponding applications and simulation results, which will attract more readers ranging from mathematicians to physicists or chemists, to name a few.
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4.3 ★★★★★
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Product Reviews
★★★★★ 5
Quality Cameras
Size: 2 Cameras
Love these Cameras. Great clear quality and super easy to set up! If you are looking to add a camera or camera system, you can't beat the price and quality of these
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Reviewed in the United States on May 18, 2026
★★★★★ 5
Read this if you're having connection or audio/video/notification difficulties ***UPDATED at end***
Before I start my revised review, let me state that there's been a lot of news lately about people hacking into Ring cameras, but this only happens when someone installs a new camera and doesn't update the default username and password (or has an extremely weak password which is easy for a hacker to guess). This is like leaving your front door open while on vacation. Your camera is sending and receiving signals over a wireless network. Anyone within range of the signal can potentially be a threat if you don't have good encryption (username and good password) set up on your camera. There's no logical reason for a Ring owner to not do this. Ring even stresses changing the default settings during the initial setup process. Bottom line, don't blame the car manufacturer if you leave the keys in your car and it gets stolen.
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Recently, I wrote a rather scathing 1 star review about the problems I was having with my new Ring Stick Up Wireless Battery Cam. I'm no stranger to wireless cams, having 10 hooked up and running seamlessly on another network as I write this, but I was totally frustrated with the connection reliability, not only with my two upper end cellphones, but also on my Galaxy Tab and Amazon Show. More times than not, the software wouldn't connect with the camera but when it did, the video was choppy. Notifications were also hit and miss. I have a great wireless mesh router system throughout the house, so after doing all the troubleshooting I could think of, I assumed it was due to faulty hardware or software. I gave up and started the return process through Amazon. It was a new product after all and new products sometimes are really buggy. Plus, I read other negative reviews which seemed to justify my thoughts and actions.
Then I got an email from a gentleman from Ring saying he read my review and asked if I'd be willing to let him help troubleshoot my issues with me. Although I had already started the return process, I was willing. It was refreshing to know Ring Customer Service was genuinely interested in troubleshooting possible defects in their newest product.
Together, we isolated the issue within about 20 minutes. It turned out it wasn't the camera or software after all.
Anyone having connection issues should do what he advised me to do. Open up the Ring app and click on the 3 little dots to the upper right of the camera screenshot, then select settings. From there go to Device Health and check the signal strength. Although I had a good mesh hub (inside) within 10 feet of my camera (mounted outside), my signal strength was RSSI -64. He stated that the signal was so weak it was on the cusp of what is needed for the camera to even minimally operate. This prompted me to reboot my wireless mesh system and reset/reconnect the camera. When it came back online, my signal strength went to -39, a vast improvement.
A quick check of all of my devices showed the camera and software working flawlessly. Hat's off to Ring.
Anyone who may be having connection or audio/video/notification difficulties, check your signal strength to the camera via the Ring software, even if your router is close by. You just might be surprised.
***UPDATE***
Camera (and software) is still working flawlessly on all devices.
Ring has now updated their Windows 10 desktop app (which previously didn't work with the new wireless battery cams) and it works flawlessly as well.
Observations.
Notifications on my phone, Tab and Amazon devices (Show, Echo, Dot) are almost instantaneous. Alexa says "Someone is at your front door." Very cool.
I bought an extra battery, but it looks like it'll be at least a few months before I need to swap it out, even with the intensive testing I've done on the Stick Up Cam. Battery life seems excellent.
I have one zone blocked out and that seems to work fine as well. I also have it mounted a couple of feet above and to the left of my front door, tilting downward at an angle. Even though residential traffic is visible in the field of view, I've not gotten one trigger due to street activity. The motion sensor is triggered by anything coming into the bottom half of it's field of view. From the time someone triggers the motion sensor until the time I'm aware of it is 1-2 seconds. That's about as close to real time as you can get. It's not given me a false alarm even once.
Telling my Amazon Show to "(Alexa), show front door cam" takes about 5 seconds to complete.
I can also watch triggered video clips and get a live feed while away from home without any extra setup to my network. It's totally automatic.
Because of the customer service I received from Ring and the fact the product is much better than I originally thought, I will be expanding my Ring family soon.
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Reviewed in the United States on October 29, 2019
★★★★★ 5
Reliable camera with solar keeps it running
Size: 1 Camera
I’ve been running this camera with the solar panel and it’s been solid. The video quality is clear day and night, and the motion alerts come through quick without a lot of false alarms. Setup was straightforward and didn’t take long.
The solar panel has been a big plus. It keeps the battery charged so I don’t have to mess with taking it down to recharge. As long as it gets decent sunlight, it stays topped off.
The app is easy to use and lets me check things anytime without issues. It’s held up well in the weather so far. Overall, it does what it’s supposed to do and gives me peace of mind. I’d recommend it if you want something low maintenance.
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Reviewed in the United States on April 14, 2026
★★★★★ 4
Just a Toy
This is a snippet from a review I provided for the Ring doorbell...
"The absolute showstopper is the horrific problem with wi-fi - a problem so consistent and acute that it renders this product useless. The doorbell and the cameras are constantly going offline, and the only way that they can be brought back online is for the user to be onsite and physically reconnect the devices. Talk about unclear on the concept! The whole idea of home security is that you want it working when you're AWAY, Amazon, not just when you're at home.
"The slightest network glitch causes the system to completely blow up: a slight power interruption, the router temporarily losing network, etc. However, every single device in my household is smart enough to come back online once the connection has been restored, except...the Ring system. Sometimes, eventually, the doorbell "figures something out" and comes back online, but the cameras? Never. They would be better off as paperweights."
I realize that there are reviews here that claim to offer fixes, but that's not the point. These cameras should behave exactly like any other wi-fi device in the house, bar none - but they don't. The signal in my house is not "weak" - I have repeaters all over the place. I have perfect signal strength on my tablets, phones, laptops, and TVs, yet the Ring software claims that - sometimes - my wi-fi signal is "weak".
Note the emphasis on the word "sometimes". Although the rest of my devices see my wi-fi signal exactly the same wherever they are, these cameras are different. I've seen indicators that have displayed everything from full signal to no signal to everything in between even though the units are positioned in the exact spot every time, no exceptions.
Besides, these reviewers need to read the part I've written here about having to be onsite to bring these units back on line. THIS...is ridiculous.
Last, but certainly not least, these cameras BLEED battery. I've had cases where I've been away a week and the motion detection has never come on and when I get back, the batteries are almost gone. This is less of an issue when the cameras have gone offline, of course, but then what's the point of having a camera with some battery left if it was never working in the first place?
If there is a way around all this, I'd like to know it, but it should come from Amazon - the vendor, not from product reviewers.
UPDATE 8-20-2023: After some great help from a customer service rep (including a replacement door chime), preliminary tests have shown that the cameras now stay online. Of course, only a long-run evaluation will do, but it does seem like things have improved.
At issue was a phemomenon called "node hopping" where the cameras seem to randomly seek out other IP addresses on the subnet then attempt to reconnect. Usually node hopping occurs when there are more devices attached to a subnet that what a router is configured to handle, but in my case, even when all my devices are attached, there are plenty of leftover addresses for the cameras to use. This is especially true when we are away where as many as six devices are actually removed from the network.
With my new Chime Pro, however, that doubles as a subrouter, the cameras are linked to this device exclusively, so node hopping is supposed to cease.
The other issue I had was due to the unusual battery drain on the cameras that I noticed when they are not active and recording. I had not anticipated that they have to remain "alive" for the user so that user can wake them up when needed, or that they wake themselves up when motion is detected. Evidently, this process requires more battery power than I had first believed. Lesson learned is that unless you want to disconnect the cameras and remove the batteries after each use, then be prepared to make sure they are fully charged up before you go away even if they have been little used previously.
Thanks again to Melissa for the support and I hope that other folks can benefit from this information.
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Reviewed in the United States on August 6, 2023
★★★★★ 5
Perfect Solution for Areas Without Electricity – Easy, Reliable, and Worth It
Size: 1 Camera, Size: 1 Camera
I have to admit, this camera brand has become my favorite. This is already my third device: I have a Ring doorbell, a wall-mounted camera, and now this battery-powered version, which turned out to be exactly what I needed for an area where I don't have access to electricity.
I installed it in the hallway of my apartment, right outside the bathroom and bedroom entrances, where there are no outlets, and it has worked perfectly for monitoring that space. It gives me great peace of mind knowing that this area is covered without having to do any complicated installations.
One of the things I like most about this brand is the image and audio quality. The image is clear both day and night, and the sound is crisp, which makes a huge difference in daily use.
The installation was quick and easy, and the app is very user-friendly. Motion notifications arrive instantly, allowing me to stay informed at all times.
It's been installed for about 15 days and the battery is around 53%, which means it will last about a month depending on usage and the amount of motion it detects.
I'm also taking advantage of the 30-day free trial, and what I find excellent is that my current $9.99 plan covers all my devices at no extra cost.It also features two-way audio, integrates seamlessly with Alexa, and has performed well so far, even outdoors.
The only thing I'd mention is that battery life is highly dependent on activity, so in busy areas it may require more frequent recharging.
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Reviewed in the United States on April 10, 2026
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