setIntegral function

Integral of Stochastic Differential Equation

'setIntegral' is the constructor of an object of class yuima.Integral

setIntegral(yuima, integrand, var.dx, lower.var, upper.var,
 out.var = "", nrow = 1, ncol = 1)

Arguments

• yuima: an object of class yuima.model that is the SDE.
• integrand: A matrix or a vector of strings that describe each component of the integrand.
• var.dx: A label that indicates the variable of integration
• lower.var: A label that indicates the lower variable in the support of integration, by default lower.var = 0.
• upper.var: A label that indicates the upper variable in the support of integration, by default upper.var = t.
• out.var: Label for the output
• nrow: Dimension of output if integrand is a vector of string.
• ncol: Dimension of output if integrand is a vector of string.

Returns

The constructor returns an object of class yuima.Integral.

References

Yuima Documentation

Author(s)

The YUIMA Project Team

Examples

## Not run:

# Definition Model

Mod1<-setModel(drift=c("a1"), diffusion = matrix(c("s1"),1,1),
  solve.variable = c("X"), time.variable = "s")

# In this example we define an integral of SDE such as
# \[
# I=\int^{t}_{0} b*exp(-a*(t-s))*(X_s-a1*s)dX_s
# \]

integ <- matrix("b*exp(-a*(t-s))*(X-a1*s)",1,1)

Integral <- setIntegral(yuima = Mod1,integrand = integ,
  var.dx = "X", lower.var = "0", upper.var = "t",
  out.var = "", nrow =1 ,ncol=1)

# Structure of slots

is(Integral)
# Function h in the above definition
Integral@Integral@Integrand@IntegrandList
# Dimension of Intgrand
Integral@Integral@Integrand@dimIntegrand

# all parameters are $\left(b,a,a1,s1\right)$
Integral@Integral@param.Integral@allparam

# the parameters in the integrand are $\left(b,a,a1\right)$ \newline
Integral@Integral@param.Integral@Integrandparam

# common parameters are $a1$
Integral@Integral@param.Integral@common

# integral variable dX_s
Integral@Integral@variable.Integral@var.dx
Integral@Integral@variable.Integral@var.time

# lower and upper vars
Integral@Integral@variable.Integral@lower.var
Integral@Integral@variable.Integral@upper.var
## End(Not run)