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Show that $X_{t} = \sqrt{c}e^{-\lambda t}\beta_{e^{2\lambda t}}$ solves $dX_{t}=\sqrt{2c\lambda}dB_{t}-\lambda X_{t}dt$

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#probability-theory #stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-differential-equations
58
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Convergence of iterated integrals in rough-path integration

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#stochastic-calculus #stochastic-integrals #rough-path-theory
608
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Combining the derivative of two Brownian motions into one.

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#stochastic-processes #stochastic-calculus #brownian-motion #levy-processes
455
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Quadratic variation and measure change

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#stochastic-calculus #brownian-motion #absolute-continuity #quadratic-variation
59
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Some Grownwall type inequality for stochastic integral equation

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#stochastic-processes #stochastic-calculus #stochastic-analysis #stochastic-differential-equations
84
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Sufficient condition for a weak solution of an SDE?

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#functional-analysis #probability-theory #stochastic-calculus #stochastic-differential-equations
19
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Stochastic integration transforms nicely under continuous time-changes.

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#reference-request #stochastic-calculus
82
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Local time formula: $L_t=\lim_{h\to0}\frac{1}{h}\int_0^t \left(P_hf(B_s)-f(B_s)\right) \text{d}s\text{ a.s.}$

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#stochastic-calculus #brownian-motion #local-time
383
Views

Showing that $X(t)=\int_0^tB(s)ds $ is a Gaussian process.

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#probability #probability-theory #stochastic-processes #stochastic-calculus #brownian-motion
803
Views

Geometric Brownian motion and its inverse

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#probability-theory #stochastic-processes #stochastic-calculus #brownian-motion #stochastic-differential-equations
138
Views

Decomposition of a stochastic process into a continuous and pure jump part

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#stochastic-processes #stochastic-calculus #stochastic-analysis
274
Views

Quadratic variation is the right variation for continuous martingales of unbounded variation

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#probability-theory #stochastic-calculus #martingales #stochastic-integrals #stochastic-analysis
1.4k
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Computing the expected value of the fourth power of Brownian motion

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#probability-theory #stochastic-processes #stochastic-calculus #martingales #stochastic-integrals
60
Views

Dealing with a term coming from Ito formula.

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#stochastic-calculus #brownian-motion #stochastic-integrals #cauchy-schwarz-inequality #stochastic-differential-equations
247
Views

Apply Ito formula to $f(B_t,S_t)=(S_t-B_t)^2$ for $t\geq0$

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#probability-theory #stochastic-processes #stochastic-calculus #martingales #stochastic-integrals

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