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There should be some way to do this with TransformedProcess (see here) but I couldn't get it to work with your bivariate process. Instead, maybe you could solve for 30 replicates of x[t], then transf …

As @MichaelE2 alluded to in his comment, DSolve isn't the best approach since you've got that noise term. Instead, take at Mathematica's stochastic differential equation functionality. In particular …

Here's a solution following @acl's suggestion of discretizing in space. I added a diffusion coefficient d and used reflecting boundary conditions. l = 1.0; (* length of domain *) nx = 101; (* number …

You could use the same trick I used here -- manually adding the noise to NDSolve instead of using RandomFunction[ItoProcess]. σx = 0.1; sol = NDSolve[{x'[t] == f[x[t], y[t]], y'[t] == g[x[t], y[t]], …

Two things: 1) You can't use {} to group terms as in your z equation. See, for example, here for more info. 2) You need to define each noise term separately. {w1, w2, w3} is a list of length three …

Here's a crazy idea: maybe it's easier to add noise to NDSolve's adaptive step size algorithms than to deal with RandomFunction[ItoProcess[]] 's fixed step size. You could use WhenEvent to perturb t …

A few things: 1) The second equation doesn't match the ODEs as noted by @b.gatessucks. 2) You need to use \[DifferentialD]t on the right hand sides. 3) x[t] approaches zero very quickly in the solu …

The strength of noise σ = 20 seems large so that it can overwhelm the mean trend. Luckily Mathematica can give some analytical insights into this stochastic process. Clear[σ] proc = StratonovichProc …

First, I changed K to k, since K is a built-in symbol. Then I ran the process for a shorter time and found that V[t] got huge: solproc = RandomFunction[proc, {0., 1.2, 0.1}, Method -> "EulerMaruyama …

I think your dt=1 solution is the wrong one. The Cos[ν t] term is very rapidly varying with your parameter value of ν=105.: Plot[Cos[ν t], {t, 0, tmax}, PlotPoints -> 200] The apparent periodic- …

You want to use RandomFunction and ItoProcess to solve these stochastic differential equations. a = 1; μ = 0.1; c = 1; σ = 0.1; sol = RandomFunction[ItoProcess[{ \[DifferentialD]s[t] == -a s[t] i[ …

From your ODE solution, it looks like there are brief bursts when x changes rapidly. This suggests a simple solution: make your step size much smaller. s = ItoProcess[{ \[DifferentialD]x[t] == \[D …

There are a few questions wrapped up here. Let me try to take them one-by-one. only one variable depends on the stochastic noise and it does not bear influence on the other part of the equation …