# Questions tagged [stochastic-processes]

A stochastic process is a random process evolving with time , i.e., a time sequence representing the evolution of some system represented by a variable whose change is subject to a random variation.

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### Where can I find Einstein's proof of the existence of atoms?

as the question states, where i can i find einstein's proof of the existence of atoms, and also, what math pre-requisites do i need to understand it deeply enough to be able to replicate it.
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### Resources on an intuitive understanding of the Girsanov Transformations

My current project involves the use of Girsanov transformation. Can anyone suggest me some resources for an intuitive understanding of the same. The pages I have been referring to (Wikipedia), deals ...
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### What is the role of the density distribution function by Liouville equation in statistical physics?

Constant density is a solution of Liouville equation which says that total derivative of density distribution functions with respect to time is zero, and it is the distribution function in ...
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### Work done by the drift term of Ornstein–Uhlenbeck process

Consider a particle obeying the Ornstein–Uhlenbeck process: $$dx_{t}=\theta (\mu -x_{t})\,dt+\sigma \,dW_{t},$$ where $x_t$ is the position of the particle at time $t$, $W_t$ denotes the Wiener ...
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### Reference Request: An introductory book on Kinetics, similar to Schroeder's on thermodynamics [duplicate]

I come from a statistics background and don't have much knowledge of physics. I need to gain bit of knowledge in statistical physics for one of the projects that I work on. I started looking at Reichl'...
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### Text Recommendation: Random Walks (for physicists)

I am an incoming graduate student in Theoretical Physics in the Netherlands, and I would like to know if any of you could recommend texts on random walks with applications to physics. My university ...
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### Reference request: Langevin dynamics of particle in high dimensional quenched random potential

I would like to have some reference (either papers or books) for the study of the Langevin dynamics (out of equilibrium, non asymptotically) of a particle $X(t)\in \mathbb{R}^N$ in a quenched random ...
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### Analytical solution to damped harmonic oscillator - Fokker-Planck equation

In the paper "Numerical solution of two dimensional Fokker-Planck equations" (available at: https://doi.org/10.1016/S0096-3003(97)10161-8), the authors quote an analytical solution to the damped ...
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### Using the Martin-Siggia-Rose (MSR) formalism for oscillator with general non-harmonicity

I am wondering if using the Martin-Siggia-Rose (MSR) formalism can be convenient/treatable for calculating correlation functions [or their spectral densities] of a linear [underdamped] oscillator with ...
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### Laplace transform of triple convolution involving Heaviside function — stems from multi-state random walk

I'm a bit stuck on this problem stemming from a multi-state random walk. I have a function of the form $$C(t) = \int_0^t dt' \theta(t'-T)A(t')B(t-t')$$ and I'd like to calculate its Laplace transform....
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### Is there a way to argue that the appearance of the dependence of past states is stochastic behavior?

Suppose in a particular set of observations that you observe what appears to be a correlation of future results based on past results. Is there a way to be certain that such a phenomena isn't just the ...
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### Second quantisation for dynamical systems

The paper "Perturbative approach to an $A + B \rightarrow C$ reaction-diffusion system", (Z. Phys. B 96, 137-144 (1994)), by Conrad and Trimper, applies the Fock Space formalism for the master ...
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### Why do we interpret the first term of the Fokker-Planck equation as drift?

With the derivation of the Fokker-Planck equation we get: $$\frac{\partial}{\partial t}P(x,t)=-\frac{\partial}{\partial x}(A(x,t)P(x,t))+\frac{1}{2}\frac{\partial^2}{\partial x^2}(B(x,t)P(x,t))$$ We ...
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### Advected Dirac comb with random number of teeth which are born and die

I'm looking for a topic which I struggle to put into words. It's a reasonable consideration which I expect has been carefully studied. I hope someone can tell me the name of it and offer some guidance ...
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### Correlation function and power spectrum of discrete time Gaussian noise summed with a time delayed version of itself

Suppose we have a process $\zeta(n) = \xi(n) + \xi(n + 1)$ Where $\xi(n)$ is discrete time white noise process, where the values taken at different times are from identically distributed Gaussian ...
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### Derivation of diffusion equation from Fokker-Planck equation

I need your help, could you please explain me the sentence "The diffusion equation is the Fokker-Planck equation for the Brownian motion". I have tried to use some assumption and transform a ...
I am studying spatial population movement and would like to model the density fluctuation by assuming a Brownian movement for each individual. Because the total number of individual ($N$) is large but ...