I What is a stochastische dynamische systeme?

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Stochastic dynamical systems refer to systems where trajectories exhibit complex, random behavior. The term "stochastic" denotes randomness, which can be inherent or arise from a lack of knowledge about a deterministic system. Financial products, such as stock prices and derivatives, serve as prime examples of these systems, often modeled using Wiener processes. These processes are characterized by continuous functions that are nowhere differentiable, leading to differential equations defined through integral equations in Ito-calculus. Understanding these systems is crucial for accurately predicting behaviors in various fields, particularly finance.
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The term "stochastic dynamical system" has a lot of different meanings. Very loosely speaking, stochastic dynamical system is a system that trajectories behave to be very complicated
 
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"Stochastic" means "random"

We can postulate the randomness directly. Alternatively, a deterministic system may appear random to us because we lack sufficiently complete knowledge of it to enable us to predict its behaviour.
 
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A typical example would be the evolution of financiel products like stock prices or derivatives. These are dynamical systems but are described by so-called Wiener processes, which are described by continuous functions which are nowhere differentiable. The resulting differential equations are not the ones you are used to, but are defined via integral equations in the so-called Ito-calculus. See e.g.

https://arxiv.org/abs/cond-mat/0408143
 
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Thread 'Off resonance driving of a MW/RF cavity'

Hello! Let's say I have a cavity resonant at 10 GHz with a Q factor of 1000. Given the Lorentzian shape of the cavity, I can also drive the cavity at, say 100 MHz. Of course the response will be very very weak, but non-zero given that the Loretzian shape never really reaches zero. I am trying to understand how are the magnetic and electric field distributions of the field at 100 MHz relative to the ones at 10 GHz? In particular, if inside the cavity I have some structure, such as 2 plates...
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