Add kernels for stochastic processes

Author: jiahao

src/StochasticProcess.jl

@@ -0,0 +1,35 @@
+# Generates Brownian motion
+BrownianProcess(dx::Real, xend::Real) = WhiteNoise(dx, xend)
+
+# Generates a white noise process
+function WhiteNoiseProcess(dx::Real, xend::Real)
+    x=[0:dx:xend]
+    dW=randn(length(x),1)*sqrt(dx)
+end
+
+# Calculates the largest eigenvalue of a stochastic Airy process
+# with Brownian noise
+function StochasticAiryProcess(dx::Real, xend::Real, beta::Real)
+    x=[0:dx:xend]
+    N=length(x)
+
+    #Discretized Airy operator
+    a=-(2/dx^2)*ones(N) - x
+    b=+(1/dx^2)*ones(N-1)
+    #Plus noise
+    dW=WhiteNoiseProcess(dx, xend)
+    a+=(2/sqrt(beta))*dW/dx
+
+    maxeig(SymTridiagonal(a,b))
+end
+
+#Sample program
+#t=10000 #number of trials
+#v=[StochasticAiryProcess(0.001, 10, 2) for i=1:t]
+#binsize=.2
+#grid=[-5:binsize:2]
+#x=hist(v, grid)
+#for i=1:length(grid)
+#    @printf("%10.5f  %8d  %s\n",grid[i],x[i],repeat("*",int(x[i]/(t*binsize)*200)))
+#end
+