Placeholder: SNIFFIN’ GLUE magazine high res photo cover by Ralph Steadman: special issue #2442 on stochastic processes, guest star: Wiener and Ito for their definitions and changes of variable: :\[dX_t = [a_1(t)X_t + a_0(t)]dt + [b_1(t)X_t + b_0(t)]dW_t, \quad X_0 \text{ donné}\]On commence par chercher une solution \(F_t\) du système homogène: \(dF_t = a_1(t)F_t dt + b_1(t)F_t dW_t\) avec \(F_0 = 1\).Trivialement :\[F_t = \exp\left[\int_0^t \left(a_1(s) - \frac{1}{2}b_1(s)^2\right)ds + \int_0^t b_1(s)dW_s SNIFFIN’ GLUE magazine high res photo cover by Ralph Steadman: special issue #2442 on stochastic processes, guest star: Wiener and Ito for their definitions and changes of variable: :\[dX_t = [a_1(t)X_t + a_0(t)]dt + [b_1(t)X_t + b_0(t)]dW_t, \quad X_0 \text{ donné}\]On commence par chercher une solution \(F_t\) du système homogène: \(dF_t = a_1(t)F_t dt + b_1(t)F_t dW_t\) avec \(F_0 = 1\).Trivialement :\[F_t = \exp\left[\int_0^t \left(a_1(s) - \frac{1}{2}b_1(s)^2\right)ds + \int_0^t b_1(s)dW_s

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SNIFFIN’ GLUE magazine high res photo cover by Ralph Steadman: special issue #2442 on stochastic processes, guest star: Wiener and Ito for their definitions and changes of variable: :\[dX_t = [a_1(t)X_t + a_0(t)]dt + [b_1(t)X_t + b_0(t)]dW_t, \quad X_0 \text{ donné}\]On commence par chercher une solution \(F_t\) du système homogène: \(dF_t = a_1(t)F_t dt + b_1(t)F_t dW_t\) avec \(F_0 = 1\).Trivialement :\[F_t = \exp\left[\int_0^t \left(a_1(s) - \frac{1}{2}b_1(s)^2\right)ds + \int_0^t b_1(s)dW_s

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SNIFFIN’ GLUE magazine high res photo cover by Ralph Steadman: special issue #2442 on stochastic processes, guest star: Wiener and Ito for their definitions and changes of variable: :\[dX_t = [a_1(t)X_t + a_0(t)]dt + [b_1(t)X_t + b_0(t)]dW_t, \quad X_0 \text{ donné}\]On commence par chercher une solution \(F_t\) du système homogène: \(dF_t = a_1(t)F_t dt + b_1(t)F_t dW_t\) avec \(F_0 = 1\).Trivialement :\[F_t = \exp\left[\int_0^t \left(a_1(s) - \frac{1}{2}b_1(s)^2\right)ds + \int_0^t b_1(s)dW_s
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