Placeholder: De façon générale, cherchons une solution de : \[ dX_t = [a_1(t)X_t + a_0(t)]dt + [b_1(t)X_t + b_0(t)]dW_t, \quad X_0 \text{ donné} \] 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 : \[ F_t = \exp\left[\int_0^t \left(a_1(s) - \frac{1}{2}b_1(s)^2\right)ds + \int_0^t b_1(s)dW_s\right] \] On va ensuite cherche une solution autour de $F_t$ en posant On pose \(Y_t = X_t/F_t\) où par Itô : \[ d\left({1\over F De façon générale, cherchons une solution de : \[ dX_t = [a_1(t)X_t + a_0(t)]dt + [b_1(t)X_t + b_0(t)]dW_t, \quad X_0 \text{ donné} \] 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 : \[ F_t = \exp\left[\int_0^t \left(a_1(s) - \frac{1}{2}b_1(s)^2\right)ds + \int_0^t b_1(s)dW_s\right] \] On va ensuite cherche une solution autour de $F_t$ en posant On pose \(Y_t = X_t/F_t\) où par Itô : \[ d\left({1\over F

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De façon générale, cherchons une solution de : \[ dX_t = [a_1(t)X_t + a_0(t)]dt + [b_1(t)X_t + b_0(t)]dW_t, \quad X_0 \text{ donné} \] 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 : \[ F_t = \exp\left[\int_0^t \left(a_1(s) - \frac{1}{2}b_1(s)^2\right)ds + \int_0^t b_1(s)dW_s\right] \] On va ensuite cherche une solution autour de $F_t$ en posant On pose \(Y_t = X_t/F_t\) où par Itô : \[ d\left({1\over F

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The rabbit (or Fibonacci) numbers form a sequence (a(1) = 1), 1, 2, 3, 5, 8,13,21,34,...,in which a(n)+2 =a(n+1) +a(n) for an y n=1,2,... . Find the greatest common divisor of the numbers a(100) and a(99).
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The value of a text extends beyond its content to include the origin of the information it contains. This origin can be rooted in significant events or the accomplishments of individuals. A text may serve as a record of an event, providing valuable documentation for future reference. It can also convey the achievements of notable individuals, whether they made groundbreaking discoveries or created influential works. It's important to note that the author of a text may not always be the person re
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